Problem: Simplify the following expression: $p = \dfrac{5t^2 + 95t + 450}{t + 9} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ p =\dfrac{5(t^2 + 19t + 90)}{t + 9} $ Then we factor the remaining polynomial: $t^2 + {19}t + {90} $ ${9} + {10} = {19}$ ${9} \times {10} = {90}$ $ (t + {9}) (t + {10}) $ This gives us a factored expression: $\dfrac{5(t + {9}) (t + {10})}{t + 9}$ We can divide the numerator and denominator by $(t - 9)$ on condition that $t \neq -9$ Therefore $p = 5(t + 10); t \neq -9$